1. Field of the Invention
The present invention relates to a method for evaluating the characteristics of a magnetic disk medium. More particularly, it relates to a method of quantitatively evaluating nonlinear transition shifts, partial erasures or the like nonlinear distortions of recorded signals, attributed to the fact that bits are recorded closely adjacent to one another in a high-density record medium.
2. Description of the Related Art
A technique called PRML (Partial Response Maximum Likelihood) has become the present-day mainstream for signal processing in the read channel of a magnetic disk device, instead of a conventional peak detection method. The PRML method is a scheme wherein PR equalization, in which the signal waveform from a head is equalized to a predetermined PR target by an equalizer, is combined with an ML method, in which NRZ data are reproduced from bit data sampled at a channel rate, by maximum-likelihood decoding. When the bit interval becomes narrow, interference of waveforms occurs, and bit detection becomes difficult with the peak detection method. In contrast, since the PRML method positively utilizes the waveform interference, bit detection at a higher line record density is possible. However, when the line record density becomes conspicuously high (the bit interval becomes conspicuously narrow), nonlinear distortion of the head signal increases, and bit detection in the PRML method becomes degraded. This is because the PR equalization is based on a linear superposition of signals. In the development of a high-record-density medium, therefore, it becomes important to precisely evaluate the magnitude of the nonlinear distortion.
Nonlinear distortion includes two sorts: A nonlinear transition shift and a partial erasure. If two magnetization transitions have been recorded in close proximity, the magnetization transition recorded later is influenced by a leakage magnetic field from the magnetization transition recorded before, and the position at which the former magnetization transition is formed shifts forward from its original position. This is called a “nonlinear transition shift”.
In addition, if two magnetization transitions have been recorded in close proximity, the amplitude of a reproduced pulse waveform based on each of the transitions becomes smaller than the amplitude in the case where the reproduced pulses of isolated waveforms are linearly superposed. This is called “partial erasure”. Partial erasure has the following two factors: One of them is ascribable to the fact that the magnetic field at a head undergoes interference on account of a demagnetic field from an adjacent bit, so the magnetization transition width of a recorded bit spreads. The other factor is ascribable to the fact that a region where magnetization is divided appears within a bit cell on account of the interaction between grains constituting the recorded layer, resulting in a decrease of the total magnetization.
Various methods have heretofore been proposed for measuring nonlinear distortion. They are classified into a time domain method and a frequency domain method. The time domain method includes a method disclosed in Dean Palmer et al., IEEE Trans. Magn., Vol. 23, pp. 2377-2379, 1987. This method is such that pseudo-random signals are recorded on a disk, the dibit response of a reproduction system is obtained by inverse convolution calculations between the input pseudo-random signals and the reproduced signal waveform thereof, and the magnitude of the nonlinear distortion is obtained from the amplitude value of an echo on a dibit response waveform attributed to a nonlinearity. The method has the advantage that all sorts of nonlinearities can be analyzed. However, it has the problems that the processing of the calculations for obtaining the dibits is complicated, and that an extreme measurement error arises when a DC offset exists in the reproduced signal waveform.
The frequency domain method includes a method called a “Harmonic Elimination method” that is disclosed by Y. Tang et al., IEEE Trans. Magn., Vol. 27, No. 6, pp. 5316-8, 1991. This method is such that a periodic pattern which contains dibits and isolated bits and in which specified odd-numbered order higher harmonic components become zero in a case where a nonlinear component is zero, and a reference pattern which contains only isolated bits, are respectively written into a disk. The reproduced signal waveforms of the patterns are frequency-analyzed to obtain the odd-numbered order higher harmonic components of the respective waveforms, and the nonlinear transition shift is evaluated in terms of the ratio between the magnitudes of the higher harmonic components. The method has the advantage that the processing is comparatively simple and easy to perform. However, it has the problem that the partial erasure and the nonlinear transition shift cannot be separated, so the nonlinear transition shift appears to become larger than its actual magnitude, under the influence of the partial erasure. Besides, the method assumes that the nonlinear transition shift is sufficiently smaller than a bit interval, and it therefore has the problem that the measurement precision of the nonlinear transition shift becomes degraded if the assumption does not hold true.
A method in which the nonlinear transition shift and the partial erasure are separately measured is disclosed by X. Che, IEEE Trans. Magn., Vol. 31, No. 6, pp. 3021-6, 1995. This method is such that the partial erasure is first obtained alone by employing a square wave signal which is not influenced by the nonlinear transition shift, while the total nonlinear distortion is obtained by the above harmonic elimination method. In addition, the nonlinear transition shift is obtained from both the obtained results. It is a method which is excellent in the point that the nonlinear distortion can be separated. For the above reason, however, it has the problem that the measurement precision of the nonlinear transition shift becomes degraded if the assumption of the nonlinear transition shift being sufficiently smaller than the bit interval does not hold true.
Another method in which the nonlinear transition shift and the partial erasure are separately measured is disclosed in Japanese publication JP-A-10-269511. This method is an improvement on the harmonic elimination method based on the fifth order harmonic. The publication discloses that a periodic pattern of 30 bits containing dibits and isolated bits is employed as a measurement pattern. The fifth order harmonic ratio between the measurement pattern and a reference pattern, which is caused to contain only isolated bits by successively changing the bit intervals of the dibits, is obtained. Partial erasure information is then obtained from the minimum value of the ratio. Further, the value of the nonlinear transition shift is obtained by employing a relational formula between the fifth order harmonic ratio and the partial erasure as well as the nonlinear transition shift. Since, however, this method necessitates means for finely adjusting the intervals of the dibits at a high precision, it is not easy to perform.
A measurement principle for the nonlinear transition shift based on the prior-art harmonic elimination method disclosed in the previously-mentioned publication by Yang et al will now be elucidated in order to supplement the embodiment of the present invention, as will be described later.
FIG. 3 shows a periodic pattern containing dibits and isolated bits, for use in the harmonic elimination method, and the reproduced signal waveform thereof. This pattern is composed of the dibits P and the succeeding isolated bits Q. Here, the term “dibit” signifies a pattern in which the magnetization transitions represents two successive bits. This pattern is represented by an NRZI (Non-Return to Zero Invert) notation, as given below. Incidentally, the “NRZI notation” is a method in which the existence of a magnetization transition is noted as “1”, whereas the nonexistence or absence of a magnetization transition is noted as “0”.
Consider the pattern 1100 . . . (m 0's)100 . . . (n 0's) 1100 . . . (m 0's)100 . . . (n 0's) (see FIG. 3). Here, m=6p and n=6q (where p and q denote natural numbers) hold true. The number of bits of this pattern is N=2 m+2n+6, and the period thereof is (2 m+2n+6)T (where T denotes the bit period of the dibits). It will be indicated below that, in a case where nonlinear distortion is nonexistent, the specified odd-numbered order higher harmonics of the reproduced signal waveform become zero.
As shown in FIG. 4, the pattern in FIG. 3 can be decomposed into three periodic patterns (a)-(c) of isolated bits. Accordingly, the reproduced signal waveform y(t) is expressed as follows:y(t)=x(t)−x(t−(n+1)T)+x(t−(n+2)T)  (1)
Here, “x(t)” denotes the temporal waveform of the periodic pattern (a) in FIG. 4.
The frequency spectrum Y(ω) of the reproduced signal waveform is expressed as:Y(ω)=X(ω)−X(ω)e−jω(n+1)T+X(ω)e−jω(n+2)T  (2)
Here, the fundamental frequency ω0 is expressed as:
                              ω          0                =                                            2              ⁢              π                        NT                    =                      π                                          (                                  m                  +                  n                  +                  3                                )                            ⁢              T                                                          (        3        )            
The kth order harmonic component is expressed as:
                                                                        Y                ⁡                                  (                                      k                                                                                                              ⁢                                              ω                        0                                                                              )                                            =                            ⁢                                                X                  ⁡                                      (                                          k                                                                                                                        ⁢                                                  ω                          0                                                                                      )                                                  -                                                      X                    ⁡                                          (                                              k                                                  ω                          0                                                                    )                                                        ·                                      ⅇ                                                                  -                        j                                            ⁢                                                                                          ⁢                                                                        k                                                                                                                                            ⁢                                                          ω                              ⁢                                                                                                                          ⁢                              0                                                                                                      ⁡                                                  (                                                      n                            +                            1                                                    )                                                                    ⁢                      T                                                                      +                                                                                                      ⁢                                                X                  ⁡                                      (                                          k                                                                                                                        ⁢                                                  ω                          0                                                                                      )                                                  ·                                  ⅇ                                                            -                      j                                        ⁢                                                                                  ⁢                                                                  k                                                                                                                                  ⁢                                                      ω                            ⁢                                                                                                                  ⁢                            0                                                                                              ⁡                                              (                                                  n                          +                          2                                                )                                                              ⁢                    T                                                                                                                          =                            ⁢                                                X                  ⁡                                      (                                          k                                              ω                        0                                                              )                                                  -                                                      X                    ⁡                                          (                                              k                                                  ω                          0                                                                    )                                                        ·                                      ⅇ                                                                  -                        j                                            ⁢                                                                        n                          +                          1                                                                          m                          +                          n                          +                          3                                                                    ⁢                      k                      ⁢                                                                                          ⁢                      π                                                                      +                                                      X                    ⁡                                          (                                              k                                                  ω                          0                                                                    )                                                        ·                                      ⅇ                                                                  -                        j                                            ⁢                                                                        n                          +                          2                                                                          m                          +                          n                          +                          3                                                                    ⁢                      k                      ⁢                                                                                          ⁢                      π                                                                                                                              (        4        )            
In the case of k=2p+2q+1, the kth order harmonic component becomes zero as indicated below:
                                                                        Y                ⁡                                  (                                      k                                          ω                      0                                                        )                                            =                                                X                  ⁡                                      (                                          k                                              ω                        0                                                              )                                                  ·                                  (                                      1                    -                                          ⅇ                                                                        -                          j                                                ⁢                                                                              n                            +                            1                                                                                m                            +                            n                            +                            3                                                                          ⁢                        k                        ⁢                                                                                                  ⁢                        π                                                              +                                          ⅇ                                                                        -                          j                                                ⁢                                                                              n                            +                            2                                                                                m                            +                            n                            +                            3                                                                          ⁢                        k                        ⁢                                                                                                  ⁢                        π                                                                              )                                                                                                        =                                                X                  ⁡                                      (                                          k                                              ω                        0                                                              )                                                  ·                                  (                                      1                    -                                          ⅇ                                                                        -                          j                                                ⁢                                                                                                            2                              ⁢                              q                                                        +                            1                                                                                                              6                              ⁢                              p                                                        +                                                          6                              ⁢                              q                                                        +                            3                                                                          ⁢                                                  (                                                                                    2                              ⁢                              p                                                        +                                                          2                              ⁢                              q                                                        +                            1                                                    )                                                ⁢                        π                                                              +                                          ⅇ                                                                        -                          j                                                ⁢                                                                                                            2                              ⁢                              q                                                        +                            2                                                                                                              6                              ⁢                              p                                                        +                                                          6                              ⁢                              q                                                        +                            3                                                                          ⁢                                                  (                                                                                    2                              ⁢                              p                                                        +                                                          2                              ⁢                              q                                                        +                            1                                                    )                                                ⁢                        π                                                                              )                                                                                                        =                                                X                  ⁡                                      (                                          k                                              ω                        0                                                              )                                                  ·                                  (                                      1                    -                                          ⅇ                                                                        -                          j                                                ⁢                                                                                                            6                              ⁢                              q                                                        +                            1                                                    3                                                ⁢                        π                                                              +                                          ⅇ                                                                        -                          j                                                ⁢                                                                                                            6                              ⁢                              q                                                        +                            2                                                    3                                                ⁢                        π                                                                              )                                                                                                        =                                                                    X                    ⁡                                          (                                              k                                                  ω                          0                                                                    )                                                        ·                                      (                                          1                      -                                              ⅇ                                                                              -                            j                                                    ⁢                                                                                                          ⁢                                                      1                            3                                                    ⁢                          π                                                                    +                                              ⅇ                                                                              -                            j                                                    ⁢                                                                                                          ⁢                                                      2                            3                                                    ⁢                          π                                                                                      )                                                  =                0                                                                        (        5        )            
Here, “k” is always an odd number, and k=5 holds true in the case of p=q=1 by way of example.
Next, it will be indicated that, in the presence of a nonlinear transition shift, the value thereof can be obtained from the kth order harmonic components of the respective reproduced signal waveforms of the periodic pattern containing the dibits and the isolated bits and the periodic pattern of the isolated bits.
In the presence of a nonlinear transition shift, the temporal waveform ŷ(t) (the reproduced signal waveform of the periodic pattern containing the dibits and the isolated bits) is expressed as follows, where Δ denotes the nonlinear transition shift:ŷ(t)=x(t)−x(t−(n+1)T+Δ)+x(t−(n+2)T+Δ))  (6)
Here, since x(t+Δ)≅x(t)+Δx(t)/dt, the following is obtained:
                                                                                                              y                    ^                                    ⁡                                      (                    t                    )                                                  =                                ⁢                                                      x                    ⁡                                          (                      t                      )                                                        -                                      x                    ⁡                                          (                                              t                        -                                                                              (                                                          n                              +                              1                                                        )                                                    ⁢                          T                                                +                        Δ                                            )                                                        +                                      x                    ⁡                                          (                                              t                        -                                                                              (                                                          n                              +                              2                                                        )                                                    ⁢                          T                                                +                        Δ                                            )                                                                                  )                                                                          =                            ⁢                                                x                  ⁡                                      (                    t                    )                                                  -                                  x                  ⁡                                      (                                          t                      -                                                                        (                                                      n                            +                            1                                                    )                                                ⁢                        T                                                              )                                                  -                                  Δ                  ·                                                            x                      ⁡                                              (                                                  t                          -                                                                                    (                                                              n                                +                                1                                                            )                                                        ⁢                            T                                                                          )                                                              /                                                                                                                                                                                                    ⁢                                                                  ⅆ                        t                                            +                                              x                        ⁡                                                  (                                                      t                            -                                                                                          (                                                                  n                                  +                                  2                                                                )                                                            ⁢                              T                                                                                )                                                                                      )                                    +                                      Δ                    ·                                          x                      ⁡                                              (                                                  t                          -                                                                                    (                                                              n                                +                                2                                                            )                                                        ⁢                            T                                                                          )                                                                                            )                            /                              ⅆ                t                                                                        (        7        )            
Let “y(t)” denote the temporal waveform of the periodic pattern containing the dibits and the isolated bits, in the absence of a nonlinear transition shift, and an error signal e(t) is defined as follows:
                                                                        e                ⁡                                  (                  t                  )                                            =                                                                    y                    ^                                    ⁡                                      (                    t                    )                                                  -                                  y                  ⁡                                      (                    t                    )                                                                                                                          =                                                                    -                    Δ                                    ·                                                            x                      ⁡                                              (                                                  t                          -                                                                                    (                                                              n                                +                                1                                                            )                                                        ⁢                            T                                                                          )                                                              /                                          ⅆ                      t                                                                      +                                  Δ                  ·                                                            x                      ⁡                                              (                                                  t                          -                                                                                    (                                                              n                                +                                2                                                            )                                                        ⁢                            T                                                                          )                                                              /                                          ⅆ                      t                                                                                                                              (        8        )            
The frequency spectrum E(ω) becomes:E(ω)=−Δ·ωX(ω)·e−jω(n+1)T+Δ·ωX(ω)·e−jω(n+2)T  (9)
The kth order harmonic component is expressed as follows:
                                                                        E                ⁡                                  (                                      k                                          ω                      0                                                        )                                            =                            ⁢                                                                                          -                      Δ                                        ·                                          k                                              ω                        0                                                                              ⁢                                                            X                      ⁡                                              (                                                  k                                                      ω                            0                                                                          )                                                              ·                                          ⅇ                                                                        -                          j                                                ⁢                                                                                                  ⁢                                                                              k                                                          ω                              0                                                                                ⁡                                                      (                                                          n                              +                              1                                                        )                                                                          ⁢                        T                                                                                            +                                                                                                      ⁢                                                Δ                  ·                                      k                                          ω                      0                                                                      ⁢                                                      X                    ⁡                                          (                                              k                                                  ω                          0                                                                    )                                                        ·                                      ⅇ                                                                  -                        j                                            ⁢                                                                                          ⁢                                                                        k                                                      ω                            0                                                                          ⁡                                                  (                                                      n                            +                            2                                                    )                                                                    ⁢                      T                                                                                                                                              =                            ⁢                                                                                          -                      Δ                                        ·                                          k                                              ω                        0                                                                              ⁢                                                            X                      ⁡                                              (                                                  k                                                      ω                            0                                                                          )                                                              ·                                          ⅇ                                                                        -                          j                                                ⁢                                                                                                  ⁢                                                                                                            2                              ⁢                              p                                                        +                                                          2                              ⁢                              q                                                        +                            1                                                                                (                                                                                          6                                ⁢                                p                                                            +                                                              6                                ⁢                                q                                                            +                              3                                                        )                                                                          ⁢                                                  (                                                                                    6                              ⁢                              q                                                        +                            1                                                    )                                                ⁢                        π                                                                                            +                                                                                                      ⁢                                                Δ                  ·                                      k                                          ω                      0                                                                      ⁢                                                      X                    ⁡                                          (                                              k                                                  ω                          0                                                                    )                                                        ·                                      ⅇ                                                                  -                        j                                            ⁢                                                                                          ⁢                                                                                                    2                            ⁢                            p                                                    +                                                      2                            ⁢                            q                                                    +                          1                                                                          (                                                                                    6                              ⁢                              p                                                        +                                                          6                              ⁢                              q                                                        +                            3                                                    )                                                                    ⁢                                              (                                                                              6                            ⁢                            q                                                    +                          2                                                )                                            ⁢                      T                                                                                                                                              =                            ⁢                                                                                          -                      Δ                                        ·                                          k                                              ω                        0                                                                              ⁢                                                            X                      ⁡                                              (                                                  k                                                      ω                            0                                                                          )                                                              ·                                          ⅇ                                                                        -                                                      j                            ⁡                                                          (                                                                                                2                                  ⁢                                  q                                                                +                                                                  1                                  3                                                                                            )                                                                                                      ⁢                        π                                                                                            +                                                                                                      ⁢                                                Δ                  ·                                      k                                          ω                      0                                                                      ⁢                                                      X                    ⁡                                          (                                              k                                                  ω                          0                                                                    )                                                        ·                                      ⅇ                                                                  -                                                  j                          ⁡                                                      (                                                                                          2                                ⁢                                q                                                            +                                                              2                                3                                                                                      )                                                                                              ⁢                      π                                                                                                                                              =                            ⁢                                                                    -                    Δ                                    ·                                      k                                          ω                      0                                                                      ⁢                                                      X                    ⁡                                          (                                              k                                                  ω                          0                                                                    )                                                        ·                                      (                                                                  ⅇ                                                                              -                            j                                                    ⁢                                                                                                          ⁢                                                      1                            3                                                    ⁢                          π                                                                    -                                              ⅇ                                                                              -                            j                                                    ⁢                                                                                                          ⁢                                                      2                            3                                                    ⁢                          π                                                                                      )                                                                                                                          =                            ⁢                                                                    -                    Δ                                    ·                                      k                                          ω                      0                                                                      ⁢                                  X                  ⁡                                      (                                          k                                              ω                        0                                                              )                                                                                                          (        10        )            
Here, from the following:E(kω0)={circumflex over (Y)}(kω0)  (11)(where Ŷ(k ω0) denotes the kth order harmonic component of the reproduced signal waveform ŷ(t) of the periodic pattern containing the dibits and the isolated bits), the nonlinear transition shift Δ eventually becomes:
                    Δ        =                                                                          E                ⁡                                  (                                      k                                          ω                      0                                                        )                                                                                                  k                                  ω                  0                                            ⁢                                                                X                  ⁡                                      (                                          k                                              ω                        0                                                              )                                                                                                =                                                                                    Y                  ^                                ⁡                                  (                                      k                                          ω                      0                                                        )                                                                                                  k                                  ω                  0                                            ⁢                                                                X                  ⁡                                      (                                          k                                              ω                        0                                                              )                                                                                                                          (        12        )            
In this manner, the nonlinear transition shift is evaluated as the ratio between the magnitudes of the kth order harmonic components of the respective reproduced signal waveforms of the periodic pattern containing the dibits and the isolated bits, and the periodic pattern of the isolated bits.
Next, a measurement procedure for the nonlinear transition shift based on the prior-art harmonic elimination method will be described.
The periodic pattern is assumed to have m=6, n=6, the number of bits N=30, and the bit period T. On this occasion, the fundamental frequency becomes ω0=2π/NT, and the higher harmonic to be eliminated becomes the fifth order harmonic.
First, the periodic pattern containing the dibits and the isolated bits (1100000001000000110000001000000) is recorded on a magnetic disk at the bit period T.
Subsequently, the periodic pattern containing the dibits and the isolated bits is read, and the magnitude |Y(5 ω0| of the fifth order harmonic component is obtained by frequency analysis.
Subsequently, the periodic pattern of the isolated bits (100000000000001000000000000000) is recorded on the magnetic disk at the bit period T.
Subsequently, the isolated-bit periodic pattern is read, and the magnitude |X(5 ω0| of the fifth order harmonic component is obtained by frequency analysis.
In addition, the nonlinear transition shift Δ is evaluated as Δ=|Y(5 ω0)|/(5 ω0×|X(5 ω0)|).
As stated above, in the prior-art harmonic elimination method, the approximation x(t+Δ)≅x(t)+Δx(t)/dt is made assuming that the nonlinear transition shift is sufficiently smaller than the bit period T. Therefore, this method has the problem that the measurement precision becomes degraded if the assumption does not hold true. Besides, this method cannot separate the partial erasure, so that the nonlinear transition shift appears to be larger than its actual magnitude in the presence of the partial erasure.
Also the method disclosed in the previously-mentioned publication by X. Che, which separately measures the partial erasure and the nonlinear transition shift, assumes that the nonlinear transition shift is sufficiently smaller than the bit period T, and it has the same problem as that of the harmonic elimination method.